最优自适应模糊复合控制研究与应用
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摘要
将模糊控制同其他领域的理论研究方法结合，利用模糊控制的优势解决该领域中常规方法难以解决的问题，实现方法的互补是模糊控制发展的一个重要方向，也是模糊系统理论领域近年来研究的热点。本文针对一类未知非线性系统的跟踪问题，提出了模糊——线性复合控制策略。该方法利用模糊逻辑系统来逼近未知非线性部分。在把逼近误差看作系统干扰的情况下，给出了模糊系统参数基于Lyapunov稳定的基础上的自适应律。但是由于模糊系统本身的缺陷，逼近误差在一定条件下有可能较大，不能忽视，而且这种逼近误差必然会影响系统的跟踪误差。所以利用系统跟踪误差构造线性最优补偿器，该补偿器用于减少逼近误差对系统跟踪误差的影响。最后证明了该方法能确保闭环系统的全局渐近稳定性而且能达到了一定的性能(如H~∞最优)要求。仿真结果进一步验证了该方法的有效性。
另外，文中给出了如何对一般的非线性系统设计该控制器的方法。并将该方法和文中所提到的控制策略应用于飞机纵向短周期控制中。仿真结果表明，用此方法，不但使设计过程简单且易于实现，而且用该方法设计出控制器可以有效地改进飞机的飞行性能，提高失速迎角，加快起恢复速度，闭环跟踪效果也令人满意。
Combining fuzzy control with classical control and modern control is of theoretical and practical significance. That is a very important direction of development of fuzzy control and a hotspot of research fuzzy system, because it can achieve complementarity of fuzzy control and other control scheme. In this paper a hybrid fuzzy-linear output tracking control schemes is developed for a class of nonlinear system. It consists of an indirect adaptive fuzzy controller, which is constructed by modeling the unknown part of system, and adaptive law given by using Lyapunov synthesis approach. Since the fuzzy descriptions are imprecise and may be insufficient to achieve the desired accuracy, it is necessary to design a compensator to removing the influence of the approximation error. So a compensator is constructed, which is compensates the approximation error's effect on system output at the condition of the approximation error thought as disturbance of the system. Finally. It is proved that the proposed control scheme can not only guarantee the asymptotic stability of the closed-loop, but also satisfy the requirement of H∞ performance index. The simulation results demonstrate and confirm the theoretical results.
In addition, we give the universal control scheme for single-in-single-out nonlinear systems in this paper. The controller for longitudinal short period model of aircraft has been designed and simulated by using those schemes. Simulation results are demonstrated to show that the scheme is not only simpleness and easy accomplish, but also enhance the performance of flight and the effectiveness and applicability of the proposed method.
另外，文中给出了如何对一般的非线性系统设计该控制器的方法。并将该方法和文中所提到的控制策略应用于飞机纵向短周期控制中。仿真结果表明，用此方法，不但使设计过程简单且易于实现，而且用该方法设计出控制器可以有效地改进飞机的飞行性能，提高失速迎角，加快起恢复速度，闭环跟踪效果也令人满意。
Combining fuzzy control with classical control and modern control is of theoretical and practical significance. That is a very important direction of development of fuzzy control and a hotspot of research fuzzy system, because it can achieve complementarity of fuzzy control and other control scheme. In this paper a hybrid fuzzy-linear output tracking control schemes is developed for a class of nonlinear system. It consists of an indirect adaptive fuzzy controller, which is constructed by modeling the unknown part of system, and adaptive law given by using Lyapunov synthesis approach. Since the fuzzy descriptions are imprecise and may be insufficient to achieve the desired accuracy, it is necessary to design a compensator to removing the influence of the approximation error. So a compensator is constructed, which is compensates the approximation error's effect on system output at the condition of the approximation error thought as disturbance of the system. Finally. It is proved that the proposed control scheme can not only guarantee the asymptotic stability of the closed-loop, but also satisfy the requirement of H∞ performance index. The simulation results demonstrate and confirm the theoretical results.
In addition, we give the universal control scheme for single-in-single-out nonlinear systems in this paper. The controller for longitudinal short period model of aircraft has been designed and simulated by using those schemes. Simulation results are demonstrated to show that the scheme is not only simpleness and easy accomplish, but also enhance the performance of flight and the effectiveness and applicability of the proposed method.
引文
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[2] Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. on.Systems, Man and Cybernetics, 1973,3(1):28～44
[3] Mamaani E H. Applications of fuzzy algorithms for simple dynamic plant. Proc.IEEE. 1974,121(12):1585～1588
[4] T. Takagi, M. Sgeno. Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Systems, Man. Cybernetic, 1985, 15:116～132
[5] 王立新 模糊系统：挑战与机会并存——十年研究之感悟自动化学报 vol27．No．4 2001
[6] L.X.Wang, Stable and Optimal Fuzzy Control of Linear Systems, IEEE Transactions on Fuzzy Systems, vol. 6, No. 1, pp. 137-143, 1998
[7] Shing-Jen Wu, Chin-Teng Lin. Optimal Fuzzy Controller Design: Local Concept Approach. IEEE Transactions on Fuzzy Systems, vol. 8, No.2, pp. 171-185, Apr, 2000
[8] Shing-Jen Wu, Chin-Teng Lin. Global Optimal Fuzzy Tracker Design Based on Local Concept Approach. IEEE Transactions on Fuzzy Systems, vol. 10, No.2, pp. 128-142, Apt, 2002.
[9] Choon-Young Lee, Ju-Jang Lee, Design of Optimal Controller for Nonlinear Systems Using Takagi-Sugeno Fuzzy Model, IEEE International Fuzzy Systems Conference Proceedings. Seoul Korea, August 22-25, 1999
[10] Kazuo TANAKA, Tsuyoshi HORI. New Robust and Optimal Designs for Takagi-Sugeno Fuzzy Control Systerns. Proceedings of the 1999 IEEE International Conference on control Applications. Kohala Coast-Island of
Hawai'I,USA. August 22-27, 1999
[11] Wea-shyong Yu and Chih-Jen sun, Fuzzy Model Based Adaptive Control for a Class of Nonlinear, IEEE Transactions on Fuzzy Systems, 2001,9(3): 413-425
[12] K. Tanaka, Y. Taniguchi and H. O. Wang, Fuzzy control based on quadratic performance function. In Proc. 37th IEEE Conf. Decision Control, Tampa,FL, 1998, pp.2914-2919
[13] K. Tanaka, T. Taniguchi, and H. O. Wang, Model-based fuzzy control of TORA system: Fuzzy regulator and fuzzy observer design via LMI's that represent decay rate, disturbance rejection, robustness, optimality. In Proc. FUZZ-IEEE.AK. 1998, pp.313-318
[14] D.Kirk, Optimal Control Theory, Prentice-Hall International, 1970
[15] L.X.Wang, Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking, IEEE Transactions on Systems Man. and Cybernetics-Part B: Cybernetics. vol. 26, pp. 667-691, October.1996
[16] 王立新 自适应模糊控制系统与控制——设计与稳定性分析 国防工业出版社2000．10
[17] Wang L X and Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning. IEEE Trans. on Neural Networks, Sept. 1992, 3(5):807～814
[18] Jang J.S, Roger J. ANFIS: adaptive-network-based fuzzy inference system[J].IEEE Trans. on Systems, Man, and Cybernetics;1993,23(3),665～685
[19] Lippmann R.A critical overview of neural network pattern classifiers. Proc.1991 IEEE Workshop on Neural Networks for Signal Procession. Princeton.NJ(1991):266～275
[20] Slotine J E. and Li W. Applied Nonlinear control. Englewood Cliffs,NJ:Prentice-Hall, Inc,1991
[21] L.X.Wang, Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking. IEEE Transactions on Systems Man. and Cybernetics-Part
B: Cybernetics. vol. 26, pp. 667-691, October.1996
[22] Wang L X. Stable adaptive fuzzy control of nonlinear systems. Proc. IEEE 1992 Conf. On Decision and Control. Tucson(1992):2511～2516
[23] Luenberger D G. Linear and Nonlinear Programming. Addison-Wesley Publishing Company. Inc., 1984
[24] L.-X. Wang, J.M. Mendel. Fuzzy basis functions universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Network 3(5)(1992) 807-814.
[25] Chi-Ying Liang, Juhng-Perng Su, A new approach to the design of a fuzzy sliding mode eontroller, Fuzzy sets and systems, 139,2003. 111～124
[26] Wang L X. and Mendel J M. Analysis and design of fuzzy logic controller. USC SIPI Report. No. 184,1991
[27] 王飞跃 关于模糊系统研究的认识和评价以及其它 自动化学报 Vol．28．N0．4，2002
[28] Wea-shyong Yu and Chih-Jen sun, Fuzzy Model Based Adaptive Control for a Class of Nonlinear, IEEE Transactions on Fuzzy Systems, 2001,9(3): 413-425
[29] Shaocheng Tong, Tao Wang, Jian Taotang, Fuzzy adaptive output tracking control of nonlinear systems, Fuzzy sets and systems 111(2000), 169～182
[30] Shaocheng Tong, Han-xing Li Direct adaptive fuzzy output tracking control of nonlinear systems, Fuzzy sets and systems 128(2002), 107～115
[31] C.-S. Chen, W.-L. Chen, Robust model reference adaptive control of nonlinear systems using fuzzy systems, Int. J. Syst. Sci. 27(12)(1996) 1435-1442.
[32] J.T. Spooner, K.M. Passino, Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Syst. 4(3)(1996)339-359.
[33] Slotine J E and Li W. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentic-Hall, Inc., 1991
[34] Tianyou Chai, Shaocheng Tong, Fuzzy direct adaptive control for a class of nonlinear
systems, Frizzy sets and systems 103(1999) 379～387
[35] Wang J, Rugh W J. Feedback Linear Systems and Linearization Families for Nonlinear Systems. IEEE Trans on Circ and Syst,1987, CAS-34(6): 650～657
[36] Wang J, Rugh W J. Feedback Linearization Families for Nonlinear Systems.IEEE Trans on Auto Contr, 1987. AC-32(10):935～940
[37] Reboulet C, Champtier C. A New Method for Linearizing Nonliear Systems:The Psendo Linearization. Int J Control. 1984,40:631～638
[38] Hunt R L, Su R, Meyer G. Global Transformation of Nonlinear Systems. IEEE Trans on Auto Contr,1983, AC-28, 24～30
[39] 范洪涛，MIMO模糊解耦方法及其在飞行控制中的应用，西北工业大学硕士论文，1997
[40] 李莉，基于T-S模型的自适应模糊系统的研究及应用，西北工业大学硕士论文，2003
[41] 胡跃明 非线性控制系统理论与应用，国防工业出版社，2002
[42] 张明廉 飞行控制系统，航空工业出版社，1994．7
[43] 张平 高金源 采用非线性系统扩展线性化方法设计飞控系统，航空学报 Vol．14 No 9．1993．9
[44] WEIJUN LIU and YONGMING LI, "OPTIMAL ADAPTIVE FUZZY CONTROL FOR A CLASS OF NONLINEAR SYSTEMS", IEEE The Second International Conference on Machine Learning and Cybernetics, Nov.2003 P628～P632
[45] 刘维军 李永明，“一类非线性系统的模糊—线性复合控制器设计” 2004 中国控制与决策学术年会(16th CDC)已录用，论文编号：CDC'04 185．
[2] Zadeh L A. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Trans. on.Systems, Man and Cybernetics, 1973,3(1):28～44
[3] Mamaani E H. Applications of fuzzy algorithms for simple dynamic plant. Proc.IEEE. 1974,121(12):1585～1588
[4] T. Takagi, M. Sgeno. Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Systems, Man. Cybernetic, 1985, 15:116～132
[5] 王立新 模糊系统：挑战与机会并存——十年研究之感悟自动化学报 vol27．No．4 2001
[6] L.X.Wang, Stable and Optimal Fuzzy Control of Linear Systems, IEEE Transactions on Fuzzy Systems, vol. 6, No. 1, pp. 137-143, 1998
[7] Shing-Jen Wu, Chin-Teng Lin. Optimal Fuzzy Controller Design: Local Concept Approach. IEEE Transactions on Fuzzy Systems, vol. 8, No.2, pp. 171-185, Apr, 2000
[8] Shing-Jen Wu, Chin-Teng Lin. Global Optimal Fuzzy Tracker Design Based on Local Concept Approach. IEEE Transactions on Fuzzy Systems, vol. 10, No.2, pp. 128-142, Apt, 2002.
[9] Choon-Young Lee, Ju-Jang Lee, Design of Optimal Controller for Nonlinear Systems Using Takagi-Sugeno Fuzzy Model, IEEE International Fuzzy Systems Conference Proceedings. Seoul Korea, August 22-25, 1999
[10] Kazuo TANAKA, Tsuyoshi HORI. New Robust and Optimal Designs for Takagi-Sugeno Fuzzy Control Systerns. Proceedings of the 1999 IEEE International Conference on control Applications. Kohala Coast-Island of
Hawai'I,USA. August 22-27, 1999
[11] Wea-shyong Yu and Chih-Jen sun, Fuzzy Model Based Adaptive Control for a Class of Nonlinear, IEEE Transactions on Fuzzy Systems, 2001,9(3): 413-425
[12] K. Tanaka, Y. Taniguchi and H. O. Wang, Fuzzy control based on quadratic performance function. In Proc. 37th IEEE Conf. Decision Control, Tampa,FL, 1998, pp.2914-2919
[13] K. Tanaka, T. Taniguchi, and H. O. Wang, Model-based fuzzy control of TORA system: Fuzzy regulator and fuzzy observer design via LMI's that represent decay rate, disturbance rejection, robustness, optimality. In Proc. FUZZ-IEEE.AK. 1998, pp.313-318
[14] D.Kirk, Optimal Control Theory, Prentice-Hall International, 1970
[15] L.X.Wang, Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking, IEEE Transactions on Systems Man. and Cybernetics-Part B: Cybernetics. vol. 26, pp. 667-691, October.1996
[16] 王立新 自适应模糊控制系统与控制——设计与稳定性分析 国防工业出版社2000．10
[17] Wang L X and Mendel J M. Fuzzy basis functions, universal approximation and orthogonal least squares learning. IEEE Trans. on Neural Networks, Sept. 1992, 3(5):807～814
[18] Jang J.S, Roger J. ANFIS: adaptive-network-based fuzzy inference system[J].IEEE Trans. on Systems, Man, and Cybernetics;1993,23(3),665～685
[19] Lippmann R.A critical overview of neural network pattern classifiers. Proc.1991 IEEE Workshop on Neural Networks for Signal Procession. Princeton.NJ(1991):266～275
[20] Slotine J E. and Li W. Applied Nonlinear control. Englewood Cliffs,NJ:Prentice-Hall, Inc,1991
[21] L.X.Wang, Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking. IEEE Transactions on Systems Man. and Cybernetics-Part
B: Cybernetics. vol. 26, pp. 667-691, October.1996
[22] Wang L X. Stable adaptive fuzzy control of nonlinear systems. Proc. IEEE 1992 Conf. On Decision and Control. Tucson(1992):2511～2516
[23] Luenberger D G. Linear and Nonlinear Programming. Addison-Wesley Publishing Company. Inc., 1984
[24] L.-X. Wang, J.M. Mendel. Fuzzy basis functions universal approximation, and orthogonal least-squares learning, IEEE Trans. Neural Network 3(5)(1992) 807-814.
[25] Chi-Ying Liang, Juhng-Perng Su, A new approach to the design of a fuzzy sliding mode eontroller, Fuzzy sets and systems, 139,2003. 111～124
[26] Wang L X. and Mendel J M. Analysis and design of fuzzy logic controller. USC SIPI Report. No. 184,1991
[27] 王飞跃 关于模糊系统研究的认识和评价以及其它 自动化学报 Vol．28．N0．4，2002
[28] Wea-shyong Yu and Chih-Jen sun, Fuzzy Model Based Adaptive Control for a Class of Nonlinear, IEEE Transactions on Fuzzy Systems, 2001,9(3): 413-425
[29] Shaocheng Tong, Tao Wang, Jian Taotang, Fuzzy adaptive output tracking control of nonlinear systems, Fuzzy sets and systems 111(2000), 169～182
[30] Shaocheng Tong, Han-xing Li Direct adaptive fuzzy output tracking control of nonlinear systems, Fuzzy sets and systems 128(2002), 107～115
[31] C.-S. Chen, W.-L. Chen, Robust model reference adaptive control of nonlinear systems using fuzzy systems, Int. J. Syst. Sci. 27(12)(1996) 1435-1442.
[32] J.T. Spooner, K.M. Passino, Stable adaptive control using fuzzy systems and neural networks, IEEE Trans. Fuzzy Syst. 4(3)(1996)339-359.
[33] Slotine J E and Li W. Applied Nonlinear Control. Englewood Cliffs, NJ: Prentic-Hall, Inc., 1991
[34] Tianyou Chai, Shaocheng Tong, Fuzzy direct adaptive control for a class of nonlinear
systems, Frizzy sets and systems 103(1999) 379～387
[35] Wang J, Rugh W J. Feedback Linear Systems and Linearization Families for Nonlinear Systems. IEEE Trans on Circ and Syst,1987, CAS-34(6): 650～657
[36] Wang J, Rugh W J. Feedback Linearization Families for Nonlinear Systems.IEEE Trans on Auto Contr, 1987. AC-32(10):935～940
[37] Reboulet C, Champtier C. A New Method for Linearizing Nonliear Systems:The Psendo Linearization. Int J Control. 1984,40:631～638
[38] Hunt R L, Su R, Meyer G. Global Transformation of Nonlinear Systems. IEEE Trans on Auto Contr,1983, AC-28, 24～30
[39] 范洪涛，MIMO模糊解耦方法及其在飞行控制中的应用，西北工业大学硕士论文，1997
[40] 李莉，基于T-S模型的自适应模糊系统的研究及应用，西北工业大学硕士论文，2003
[41] 胡跃明 非线性控制系统理论与应用，国防工业出版社，2002
[42] 张明廉 飞行控制系统，航空工业出版社，1994．7
[43] 张平 高金源 采用非线性系统扩展线性化方法设计飞控系统，航空学报 Vol．14 No 9．1993．9
[44] WEIJUN LIU and YONGMING LI, "OPTIMAL ADAPTIVE FUZZY CONTROL FOR A CLASS OF NONLINEAR SYSTEMS", IEEE The Second International Conference on Machine Learning and Cybernetics, Nov.2003 P628～P632
[45] 刘维军 李永明，“一类非线性系统的模糊—线性复合控制器设计” 2004 中国控制与决策学术年会(16th CDC)已录用，论文编号：CDC'04 185．